Improvements of jackknife confidence limit methods

Abstract

SUMMARY Edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method. Adjustments to the usual jackknife confidence limit formulae are obtained. This approach is contrasted with a bootstrap approach in numerical illustrations for estimation of a ratio. Jackknife methods are nonparametric methods for estimating the bias and standard error of an estimate T. Approximate confidence limits for the estimand can be found by using a large-sample normal approximation for T. Somewhat curiously, little is known about possible improvements to the normal approximation in this context, although improvements based on Edgeworth expansions are familiar in other problems. In this paper we show that Edgeworth expansion methods can be applied in the jackknife context. Numerical results for a particular application raise the possibility that the resulting improvements of jackknife methods can be matched by a suitable use of bootstrap methods (Efron, 1982).